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Simplifying 0.5(d + -3) = 0.4d + 6 + -1 + 0.6d Reorder the terms: 0.5(-3 + d) = 0.4d + 6 + -1 + 0.6d (-3 * 0.5 + d * 0.5) = 0.4d + 6 + -1 + 0.6d (-1.5 + 0.5d) = 0.4d + 6 + -1 + 0.6d Reorder the terms: -1.5 + 0.5d = 6 + -1 + 0.4d + 0.6d Combine like terms: 6 + -1 = 5 -1.5 + 0.5d = 5 + 0.4d + 0.6d Combine like terms: 0.4d + 0.6d = 1d -1.5 + 0.5d = 5 + 1d Solving -1.5 + 0.5d = 5 + 1d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1d' to each side of the equation. -1.5 + 0.5d + -1d = 5 + 1d + -1d Combine like terms: 0.5d + -1d = -0.5d -1.5 + -0.5d = 5 + 1d + -1d Combine like terms: 1d + -1d = 0 -1.5 + -0.5d = 5 + 0 -1.5 + -0.5d = 5 Add '1.5' to each side of the equation. -1.5 + 1.5 + -0.5d = 5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.5d = 5 + 1.5 -0.5d = 5 + 1.5 Combine like terms: 5 + 1.5 = 6.5 -0.5d = 6.5 Divide each side by '-0.5'. d = -13 Simplifying d = -13
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